Do you have to touch both starting and ending lines for the SDC when taking the ACFT?

No to your question about 'touching' the line, but for all portions it is impractical, if not impossible, to continue to the next one without the Soldier crossing the starting line.

As there have been many updates/changes to the ACFT since it was initially rolled out, a quick source on the update info is the Army's ACFT webpage*. Scroll down to "Sprint-Drag-Carry" and click on "Proper Technique and safety tips".

Sprint portion - the standard at the 25-meter line is that the Soldier will "touch hand and foot to the ground on or over the line" before sprinting back to the finish/start line. If this is the final portion of the event, the time stops when the Soldier crosses the line.

Drag portion - the standard on the 25-meter line is that "the entire sled crosses the 25m line" and then returning to beyond the starting line until "the entire sled crosses the start line" before moving to the next portion.

Some are confused by this as the instructions the NCOIC reads for the event states that you need to drag the sled entirely past the 25m line ("For the second shuttle, grasp each pull-strap handle to pull the 90-pound sled backwards until the whole sled crosses the 25-meter line"), but doesn't say that for the return leg ("Turn and drag the sled back to the start line").

Lateral portion - the standard for the 25-meter line is "touch the 25m line with foot and hand" before returning to the start line.

Carry portion - the standard at the 25-meter line is that the Soldier will "step on or over the line with one foot" and return to the starting line and "step on or over it" and that the kettlebells must be placed on the ground and cannot be thrown or dropped.
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* ATP 7-22.01, C2 - https://armypubs.army.mil/epubs/DR_pubs/DR_a/ARN35869-ATP_7-22.01-002-WEB-5.pdf
* Army's ACFT main page - https://www.army.mil/acft

"You must assume the prone position with hands on the ground beneath your shoulders
and with the top of your head behind the start line, ready to complete 5 consecutive
and continuous 50-meter shuttles. For the first shuttle, on the command, “GO,” stand
up and sprint 25 meters before touching the 25-meter line with your foot and hand,
turning at the line and sprinting back to the start. If you fail to touch properly, the grader
will call you back before allowing you to continue. For the second shuttle, grasp each
pull-strap handle to pull the 90-pound sled backwards until the whole sled crosses the
25-meter line. If you fail to cross the line with the sled, the grader will call you back
before allowing you to continue. Turn and drag the sled back to the start line. For the
third shuttle, you will perform the lateral for 25 meters, touching the line with foot and
hand before performing the lateral back to the start line. The lateral will be performed
leading with the left foot in one direction and the right foot in the other direction. For
the fourth shuttle, grasp the handles of the two 40-pound kettlebells and run 25 meters,
touching the line with the foot before returning back to the start line. Place the
kettlebells on the ground without dropping them. For the fifth shuttle, sprint 25 meters
to the line, touching with the foot and hand before turning and sprinting back to the
start line to complete the event."

You are crossing the shuttle at the start and I've never heard having to touch it when you go back to the start for each iteration but you have to cross it to get the sled, cross both ends with the sled, cross both ends with KBs and then you cross it at the finish.

Is someone saying you have to touch the line at the start of each iteration? Where did they get that from?